The DNA match that the author claims is very suspect. Here is a good article about why. The bullet points are:
Shawl:
There was no contemporary documentation that the shawl was recovered from the crime scene
There was no contemporary documentation that the Inspector that supposedly took the shawl and gifted it to his wife was at the crime scene
The shawl was silk and had an expensive design making it unlikely that Eddowes would have owned it
DNA:
The DNA collected and compared was mitochondrial DNA which is far less unique than nuclear DNA, mitochondrial DNA is generally considered exclusory rather than inclusory
The shawl was not kept free from contamination, descendents of both the identified victim and the identified suspect are known to have handled the shawl prior to testing
On top of the problematic DNA match from his last book the author is now layering on conspiracy theories concerning Freemasons and antisemitism for his new book to draw even more questionable conclusions.
Mary Pearcey, like many other famous Victorian-era murderers, has been suggested as a suspect in the Jack the Ripper slayings. She was apparently the only female suspect mentioned at the time. Sir Arthur Conan Doyle, creator of Sherlock Holmes, speculated at the time that the Ripper might have been female, as a woman could have pretended to be a midwife and be seen in public in bloody clothing without arousing suspicion or notice.
This theory was then expanded upon in 1939 by William Stewart in his book Jack the Ripper: A New Theory, which specifically named Pearcey in connection with the crimes. All evidence given is circumstantial, and there is no physical evidence or eyewitness reports linking Pearcey to the Ripper crimes.
F. Tennyson Jesse, the British criminal historian, explained the theory in her study of Pearcey's case: "It was no wonder that, simultaneously with the discovery of the crime, legends should have sprung up around her figure. The rumour even arose that the notorious Jack the Ripper had been at work in the locality, and though this was quickly disproved, yet the violence and horror associated with the crime was such as to make it understandable how the rumour arose in the first place. Even in the earliest paragraphs which announced the discovery of the crime, several false statements were suggested."
In May 2006, DNA testing of saliva on stamps affixed to letters allegedly sent by Jack the Ripper to London newspapers, and thought by some modern writers to be genuine, appeared to come from a woman. This led to extensive discussion of Pearcey and her crime in the global press.
I don't know who it was, but my dad was very interested in the case and was convinced there was a Salvation Army connection for reasons I don't remember, but then years after he told me that, this came up:
Yeah but those don't usually go unsolved for 150 years and it seems very unlikely that any of the British historians involved in this project would be able to make enough meaningful changes to the American sociopolitical landscape to offer any help on that subject.
Jack the Ripper was the first well-known case of a serial killer. There were previous serial killers, but their killings did not have the international publicity that Jack the Ripper had. It was perfect newspaper fodder given the seedy location of urban London and the lurid details of the murders of prostitutes coupled with things like telegraph cables covering the world and crossing the oceans. And, as others have said, it was never solved.
So obviously people have wanted a resolution to something like that for decades.
There are things worse than that, even. And those things invalidate discussion of american school shootings as much as the shootings should invalidate this discussion.